Acceleration is the key, not momentum, which explains why the shortened backswing can still produce so much power. The power comes from a rapid change of direction and speed (as in martial arts): from the ball to the shoulder, pulling across with the biceps and pectorals, and even pulling back towards the fence behind you - not momentum from the take-back to the ball and stepping in (forward) which causes a braking or deceleration. Experiment on court with this (open stance FH) pulling up, across and back - keep the racket in front of your body as long as possible, then move slowly to the ball until you feel it on the strings, then pull hard from contact to the finish - as if 5 mph taking the racket back, 15 mph approaching the ball and 50 mph from the ball to the shoulder. Your weight will transfer from the outside (loaded) leg to the opposite leg as you pull ACROSS your body, not forward. You will rip the shot!

This page has a good explanation of the critical role that net force plays in the modern topspin FH. Tennis is a vertical game, and for that reason the unbalanced aspect of net force in upward, across and even to some degree backwards movement is key.

This page has a good explanation of the critical role that net force plays in the modern topspin FH. Tennis is a vertical game, and for that reason the unbalanced aspect of net force in upward, across and even to some degree backwards movement is key.

This page has a good explanation of the critical role that net force plays in the modern topspin FH. Tennis is a vertical game, and for that reason the unbalanced aspect of net force in upward, across and even to some degree backwards movement is key.

Of course there is weight transfer going forward even if it's not the main transfer. He's not falling backwards and rotating. He's rotating and moving at an angle. He's not sliding his body at an direct angle. You can't rotate your body as Roger does in that picture without weight transfer. In the golf swing I would call that out and around rotation. Look at his right shoulder position at the end of the shot. He's turned into the shot...not cut off his finish and turned/slid left of the shot.

Of course there is weight transfer going forward even if it's not the main transfer. He's not falling backwards and rotating. He's rotating and moving at an angle. He's not sliding his body at an direct angle. You can't rotate your body as Roger does in that picture without weight transfer. In the golf swing I would call that out and around rotation. Look at his right shoulder position at the end of the shot. He's turned into the shot...not cut off his finish and turned/slid left of the shot.

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Not really the point though. His net movement is away from the direction of shot.

Lots of folks respect Rod Cross' work on this.
His models use only the mass of racket, as he says that is the only racket mass going into the shot. His his assumption correct?

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It isn't an assumption. It is truth. At the point of contact, the mass of the racquet is the only mass involved in launching the ball. Although technically, the mass/inertia of the ball is also involved. The momentum of the racquet is also involved.

At each point in the chain, there is mass and acceleration/momentum involved.

Not really the point though. His net movement is away from the direction of shot.

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Sure it is. The claim is that there is no weight transfer forward at all during the shot. He finishes away from the direction of the shot, but it's not a simple slide from left to right. He rotates his body forward finishing left as opposed to not rotating and sliding left or not rotating and stepping forward towards the target. I know you're an MTM guy so if you watch Oscar demonstrate a WW fh his finish is left. But, the rotation carries him through the hitting area with 'some' forward momentum before it completes the rotation leaving him left of the target.

This is a great discussion. It really makes you think about what is happening.

Sure it is. The claim is that there is no weight transfer forward at all during the shot. He finishes away from the direction of the shot, but it's not a simple slide from left to right. He rotates his body forward finishing left as opposed to not rotating and sliding left or not rotating and stepping forward towards the target. I know you're an MTM guy so if you watch Oscar demonstrate a WW fh his finish is left. But, the rotation carries him through the hitting area with 'some' forward momentum before it completes the rotation leaving him left of the target.

This is a great discussion. It really makes you think about what is happening.

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I agree there is merit to your points. You may have noticed statements to that effect several times during this thread.
But as this thread has progressed, the idea of getting to the shot by getting into the court was the main pt of contention,
starting with this post below:

"Fed's feet are behind the baseline when he begins stroke and they are clearly inside the baseline at the end of it. That's weight transfer."

So what I was explaining is that really no one is debating against what you have said and that the movement of the body towards the ball/shot, is really the only thing where there is disagreement. That poster seemed to think that since Fed had moved slightly into the court, it meant more towards line of shot; but didn't realize Fed's feet had clearly moved to something closer to 160-180 out from the line shot.

It isn't an assumption. It is truth. At the point of contact, the mass of the racquet is the only mass involved in launching the ball. Although technically, the mass/inertia of the ball is also involved. The momentum of the racquet is also involved.

At each point in the chain, there is mass and acceleration/momentum involved.

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So since you agree with that assumption, as many do, then wouldn't that prove that there is no need for the players body wt to be in a given direction, as long as he can move the racket for a certain acceleration (or speed if you are in that camp)?

It isn't an assumption. It is truth. At the point of contact, the mass of the racquet is the only mass involved in launching the ball. Although technically, the mass/inertia of the ball is also involved. The momentum of the racquet is also involved.

At each point in the chain, there is mass and acceleration/momentum involved.

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When bodies are connected together, you cannot isolate one and say that is the only mass responsible. It has been shown that the "virtual racquet" extends up to the lower part of the forearm.

The momentum of the racquet is not separate from other momentum of the body. That is why cricket players runs many yards before bowling (pitching) the ball. The speed built up by the body also contributes to the speed of the ball. A rock thrown at someone by a crazed teenager from a moving car is far more devastating that one thrown by him if he was still.

I agree there is merit to your points. You may have noticed statements to that effect several times during this thread.
But as this thread has progressed, the idea of getting to the shot by getting into the court was the main pt of contention,
starting with this post below:

"Fed's feet are behind the baseline when he begins stroke and they are clearly inside the baseline at the end of it. That's weight transfer."

So what I was explaining is that really no one is debating against what you have said and that the movement of the body towards the ball/shot, is really the only thing where there is disagreement. That poster seemed to think that since Fed had moved slightly into the court, it meant more towards line of shot; but didn't realize Fed's feet had clearly moved to something closer to 160-180 out from the line shot.

A clear example of weight transfer is something I observed up close recently - Vera Zvonereva leaning on her down the line backhand. Amazing speed of the ball results from this, and left us (in the audience) gasping. Always look to the pros to find out what is really going on - other arguments are meaningless.

When bodies are connected together, you cannot isolate one and say that is the only mass responsible. It has been shown that the "virtual racquet" extends up to the lower part of the forearm.

The momentum of the racquet is not separate from other momentum of the body. That is why cricket players runs many yards before bowling (pitching) the ball. The speed built up by the body also contributes to the speed of the ball. A rock thrown at someone by a crazed teenager from a moving car is far more devastating that one thrown by him if he was still.

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Where is that shown? I'm interested in this.

I guess the question this begs is;
does the running or car spd add to the mass?
or does it add to the acceleration potential?
or both?

For the guy in a car, the speed at which he can throw is the same as if he is stationary. But when this gets added to the speed of the car, it becomes formidable. It has been documented by the police. The teenage boy did not realize how fast his missile was going because he thought it would be the same as the prank he played on his brother at home by throwing something at him.

The mass is added even if stationary.

In cricket, it may be more complicated, because the running just does not add speed to the ball, but also probably preps up internal muscles and actually increases the throwing speed to much more than the stationary case. So, it is not simply (man running speed + stationary throwing speed) but the second quantity is itself going to be much larger.

For the guy in a car, the speed at which he can throw is the same as if he is stationary. But when this gets added to the speed of the car, it becomes formidable. It has been documented by the police. The teenage boy did not realize how fast his missile was going because he thought it would be the same as the prank he played on his brother at home by throwing something at him.

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This has also been documented by Newton. Motion is generally relative (excepting near the speed of light which we could have a fascinating discussion about, and forms the basis for special relativity). We are, after all, living on a roundish globe spinning 'round the sun, our shared "reference frame".

This topic has been discussed many times in different contexts, and this is the way I understand it, in simple terms.

The unwinding of a coiled body aided by the leg push off creates a lag in the arm and hand, loading the shoulder and arm muscles. The contraction of the stretched muscles, aided by the pull from the rotating body, accelerates the arm in the forward swing. My claim is that at this point, the body has transferred whatever energy it will to the hand/racquet system, and its only remaining function is to serve as a solid anchor from which the arm and hand can do their job to add more energy to the racquet. This is where the positioning of the arm becomes important - the hand body connection must be solid. If your arm is flailing wildly at this point, it will not have enough support from the body, and your shot will not feel solid. All the advice about how to position the hand/wrist correctly comes in at this point. Upper arm rotation and biceps contraction provide the main additional racquet head speed at this point, with ulnar to radial movement of wrist adding to spin and control (and some power, of course).

Actual forward movement of the body at contact time, in terms of MPH, is probably not contributing anything significant, and as long as it provides a solid base for the arm, it can be moving in any direction appropriate for the shot. In some very short strokes such as volleys and certain approach shots, I think body movement forwards probably ensures that the racquet goes through the range of motion that's necessary, and that the player is not standing in one spot and reaching forwards. Of course, such movement also helps the player get positioned early for the next shot, as we know.

This has also been documented by Newton. Motion is generally relative (excepting near the speed of light which we could have a fascinating discussion about, and forms the basis for special relativity). We are, after all, living on a roundish globe spinning 'round the sun, our shared "reference frame".

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Motion is also relative near the speed of light. The addition of velocities is not Galilean, but involves a non-linear term. It is still relative. Two high speed electron beams moving towards each other at 0.8c will not see a relative speed of 1.6c, but only 0.98c. So it is still relative and not the original speed of each.

It is only light, or photons in general, whose motion is not relative and the speed is always c.

When bodies are connected together, you cannot isolate one and say that is the only mass responsible. It has been shown that the "virtual racquet" extends up to the lower part of the forearm.

The momentum of the racquet is not separate from other momentum of the body. That is why cricket players runs many yards before bowling (pitching) the ball. The speed built up by the body also contributes to the speed of the ball. A rock thrown at someone by a crazed teenager from a moving car is far more devastating that one thrown by him if he was still.

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I said "at the point of contact" the only mass directly involved is the racquet. The rest is all acceleration or momentum.

What I have said consistently about a hundred thousand times is that at every point in the stroke, there is a mass and an acceleration involved. In the entire chain, I contend that the mass at the beginning is actually the most impactful -- which is body weight itself.

I said "at the point of contact" the only mass directly involved is the racquet. The rest is all acceleration or momentum.

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The point of contact is on the strings (unless you are like me and believe in using all that you paid for). Then why does the racquet mass come into play? Because the racquet is connected to the strings. In the same way, anything connected to the racquet also comes into play, in lesser and lesser amounts (like the mass of your head may not be significant). Otherwise only the mass of the string area in contact, which is negligible, would be the mass involved.

There are a lot of debates about optimum racquet mass and how much tennis player’s body mass should be behind the striking racquet. Let’s assume:Tennis boll has the mass 0.057 kg. Vreal - is the speed of the ball after impact with the racket with real mass (real racquet).Videal - is the ball speed after impact with the racket with infinite mass (ideal racquet).Then, the tennis racquet mass efficiency can be expressed as:K = Vreal/Videal.I don’t want to write any more formulas here and show just result of calculation of racquet mass efficiency.

We can see from the diagram above, the racquet alone (0.3-0.4kg) can provide mass efficiency 84-87.5%. The racquet with hand (1-1.5kg) has efficiency 94-97%. The racquet mass efficiency with the arm would be more 98%. Thus, the mass of the body behind the racquet is not so important. IMO, mass of the hand and forearm would be enough.

Argh, we're going in circles. I have to give up on this thread. Too many people are not understanding mechanical physics and I'm fairly sure that a single thread isn't going to properly educate people.

The point of contact is on the strings (unless you are like me and believe in using all that you paid for). Then why does the racquet mass come into play? Because the racquet is connected to the strings. In the same way, anything connected to the racquet also comes into play, in lesser and lesser amounts (like the mass of your head may not be significant). Otherwise only the mass of the string area in contact, which is negligible, would be the mass involved.

There are a lot of debates about optimum racquet mass and how much tennis player’s body mass should be behind the striking racquet. Let’s assume:Tennis boll has the mass 0.057 kg. Vreal - is the speed of the ball after impact with the racket with real mass (real racquet).Videal - is the ball speed after impact with the racket with infinite mass (ideal racquet).Then, the tennis racquet mass efficiency can be expressed as:K = Vreal/Videal.I don’t want to write any more formulas here and show just result of calculation of racquet mass efficiency.

We can see from the diagram above, the racquet alone (0.3-0.4kg) can provide mass efficiency 84-87.5%. The racquet with hand (1-1.5kg) has efficiency 94-97%. The racquet mass efficiency with the arm would be more 98%. Thus, the mass of the body behind the racquet is not so important. IMO, mass of the hand and forearm would be enough.

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Does this prove Cross wrong, or just show how the racket is most of the mass (85%) needed?

Is the ref for this chart solid?
So more mass after a point does not matter much?

How do you factor in the grip (how tight the racquet is being held), seems to be that this would be a critical factor and might negate/alter some of the calculations everyone is talking about.

Would everyone agree that the amount the racquet is "forced back" at impact is a factor of the speed/pace of the incoming shot, the weight of the racquet, the speed of the racquet coming forward at impact, trampoline effect of the strings, weight of the player - where/how does grip fit in (has to be a significant factor)?

Do all the equations take this into consideration and if so, how?

Isn't there also a "time" element involved - however small?

Just trying to understand the "practical" implications of what everyone is talking about.

How do you factor in the grip (how tight the racquet is being held), seems to be that this would be a critical factor and might negate/alter some of the calculations everyone is talking about.

Would everyone agree that the amount the racquet is "forced back" at impact is a factor of the speed/pace of the incoming shot, the weight of the racquet, the speed of the racquet coming forward at impact, trampoline effect of the strings, weight of the player - where/how does grip fit in (has to be a significant factor)?

Do all the equations take this into consideration and if so, how?

Isn't there also a "time" element involved - however small?

Just trying to understand the "practical" implications of what everyone is talking about.

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I think the calcs do take it into account by addressing max potential values and anything less than optimal grip would reflect by depressing the values.

I'm thinking the bold above is why accel is important, as this would suffer less at impact than just straight velocity I expect.

There are a lot of debates about optimum racquet mass and how much tennis player’s body mass should be behind the striking racquet. Let’s assume:Tennis boll has the mass 0.057 kg. Vreal - is the speed of the ball after impact with the racket with real mass (real racquet).Videal - is the ball speed after impact with the racket with infinite mass (ideal racquet).Then, the tennis racquet mass efficiency can be expressed as:K = Vreal/Videal.I don’t want to write any more formulas here and show just result of calculation of racquet mass efficiency.

We can see from the diagram above, the racquet alone (0.3-0.4kg) can provide mass efficiency 84-87.5%. The racquet with hand (1-1.5kg) has efficiency 94-97%. The racquet mass efficiency with the arm would be more 98%. Thus, the mass of the body behind the racquet is not so important. IMO, mass of the hand and forearm would be enough.

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wow - this is the scientific way of saying - swing the HUMAN racket, not the graphite racket !

There are a lot of debates about optimum racquet mass and how much tennis player’s body mass should be behind the striking racquet. Let’s assume:Tennis boll has the mass 0.057 kg. Vreal - is the speed of the ball after impact with the racket with real mass (real racquet).Videal - is the ball speed after impact with the racket with infinite mass (ideal racquet).Then, the tennis racquet mass efficiency can be expressed as:K = Vreal/Videal.I don’t want to write any more formulas here and show just result of calculation of racquet mass efficiency.

We can see from the diagram above, the racquet alone (0.3-0.4kg) can provide mass efficiency 84-87.5%. The racquet with hand (1-1.5kg) has efficiency 94-97%. The racquet mass efficiency with the arm would be more 98%. Thus, the mass of the body behind the racquet is not so important. IMO, mass of the hand and forearm would be enough.

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This is consistent with what I have read before that the virtual racquet extends up to the forearm.

But one needs to be careful in the interpretation. A bent over club player with bad balance cannot achieve this racquet efficiency. His strokes will never be as powerful as that of a pro who is properly positioned beyond the ball.

The phrase "leaning on the stroke" probably refers to proper positioning and not actually influencing ball power with your weight.

I think the calcs do take it into account by addressing max potential values and anything less than optimal grip would reflect by depressing the values.

I'm thinking the bold above is why accel is important, as this would suffer less at impact than just straight velocity I expect.

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Well, not really because seldom are we gripping the racquet so tight that there isn't "some" movement at this spot/point/joint. For instance when a player at net attempting a drop volley they should have very little pressure on the grip. The grip, as we all know, isn't some mechanical device that we can tighten with a wrench so depending on the player, the effect/result of the grip will determine the extent of the rebound off the racquet.

I think this is "might" be illustrated by when we catch the ball on the racquet - the ball doesn't go anywhere. I realize we're trying to match the speed of the ball with the racquet head in this case, but this might represent the far end of the spectrum.

As far as acceleration is concerned it seems we're back to the old basic engineering question of: will as much force be generated by a car going 60 MPH as one that is still accelerating but has just reached 60 MPH?

Well, not really because seldom are we gripping the racquet so tight that there isn't "some" movement at this spot/point/joint. For instance when a player at net attempting a drop volley they should have very little pressure on the grip.

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I don't get your point here.
You are just restating what I said about "anything less less than an optimal grip will result in depressed values."
Your example of a drop volley would be less than optimal grip (although purposefully), resulting in a depressed value for the contribution of forearm and hand.
Right?

As far as acceleration is concerned it seems we're back to the old basic engineering question of: will as much force be generated by a car going 60 MPH as one that is still accelerating but has just reached 60 MPH?

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I can share that on my motorcycle, I had much rather be at a steady state 60 mph if I am forced to make a very quick stop for brake lights. It is one of the many things I've learned to enhance safety when riding.
When caught in heavy acceleration, even at a slower speed,
it is much more to control and get stopped than at a steady state cruising speed.

This is consistent with what I have read before that the virtual racquet extends up to the forearm.

But one needs to be careful in the interpretation.

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I think you are correct that we must be very careful.

This chart may be the consistent source of this idea circulating in many directions, but from only one study/interpretation.

Also, we have to be careful in working to realize what will give the max values.
Does bent or balance have anything to do with adding mass value to the racket?
Not saying it doesn't, but don't want to assume this. It would be very interesting to see what the source of that chart had to say about obtaining max hand/ arm contributions.

I don't get your point here.
You are just restating what I said about "anything less less than an optimal grip will result in depressed values."
Your example of a drop volley would be less than optimal grip (although purposefully), resulting in a depressed value for the contribution of forearm and hand.
Right?

Ok,
so how did you figure the hand and arm for small contributions? and

body for none?

what did you feel resulted in the most hand and forearm contributions?

thanks

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I'm guessing he just did a calculation based on conservation of momentum and kinetic energy. Noting the already large difference in the relative mass of the racket and ball, the marginal contribution (to the outgoing ball speed) of additional mass is pretty small. I did a little spreadsheet calculation and got the same result. toly might have done something fancier, I just used the math in this: http://en.wikipedia.org/wiki/Elastic_collision

Explaining how drop shots work probably does require a little more elaborate theory regarding how a player might reduce the "efficiency" of the ball-racket collision (since a simple bounce off a still, firmly held racket results in a pretty high outgoing ball velocity).